Subgroups — #36572026

Order 22784.

692 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028912	C₂	1	1	yes	maximal, characteristic
2	#26028910	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151634	C₂	1	1	yes	maximal, characteristic
4	#26021004	C₂	1	2	yes	maximal, complemented
5	#26020854	C₂	1	2	yes	maximal, complemented
6	#26020849	C₂	1	2	yes	maximal, complemented
7	#26020352	C₂	1	1	yes	maximal, characteristic
8	#26020288	C₂	1	1	yes	maximal, characteristic
9	#26020135	C₂	1	2	yes	maximal, complemented
10	#26020030	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1826	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10623494	C₂²	1	1	yes	characteristic
13	C₂×#15667971	C₂²	1	1	yes	characteristic
14	#19151659	—	2	2	no	—
15	#19151656	—	2	2	no	—
16	#19151655	—	2	1	no	—
17	#19151652	—	2	1	no	—
18	#19151651	—	2	1	no	—
19	#19151648	—	2	1	no	—
20	C₂×#15667947	C₂²	1	2	yes	—
21	#19151634	C₄	1	1	yes	characteristic, complemented
22	#19151634	C₄	1	1	yes	characteristic, complemented
23	#19151634	C₄	1	1	yes	characteristic, complemented
24	#19151634	C₄	1	1	yes	characteristic, complemented
25	#19151634	C₂²	1	1	yes	characteristic
26	#19151634	C₂²	1	1	yes	characteristic
27	#19151634	C₂²	1	1	yes	characteristic
28	#19151634	C₂²	1	1	yes	characteristic
29	C₂×#15667945	C₄	1	1	yes	characteristic, complemented
30	C₂×#15667945	C₄	1	1	yes	characteristic, complemented
31	C₂×#15667943	C₄	1	1	yes	characteristic, complemented
32	C₂×#15667943	C₄	1	1	yes	characteristic, complemented
33	#19151626	C₂²	1	2	yes	—
34	#19151625	C₂²	1	2	yes	—
35	#19151562	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
37	#19151556	C₂²	1	2	yes	—
38	#19151554	C₂²	1	2	yes	—
39	C₂×#15667923	C₂²	1	2	yes	—
40	#19151362	C₂²	1	2	yes	—
41	#19151358	C₂²	1	2	yes	—
42	#19151358	C₂²	1	2	yes	—
43	#19151353	C₂²	1	2	yes	—
44	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
45	#407×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
47	#339×C₈₉	C₂²	1	2	yes	—
48	#339×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083558	C₂³	1	2	yes	—
50	C₂²×#10623494	—	2	4	no	—
51	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
52	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
53	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
55	C₂²×#10623494	C₂³	1	1	yes	characteristic
56	C₂²×#10623494	C₂³	1	2	yes	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	#15667971	—	2	1	no	—
59	#15667971	—	2	1	no	—
60	#15667971	C₂×C₄	1	1	yes	characteristic
61	#15667971	C₂×C₄	1	1	yes	characteristic
62	#15667971	C₂³	1	1	yes	characteristic
63	#15667971	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
67	C₂×C₄×Dic₈₉	—	2	1	no	—
68	#15667947	—	2	4	no	—
69	#15667945	C₂×C₄	1	1	yes	characteristic
70	#15667945	C₂×C₄	1	1	yes	characteristic
71	#15667945	C₂×C₄	1	1	yes	characteristic
72	#15667945	C₂×C₄	1	1	yes	characteristic
73	#15667945	C₂×C₄	1	1	yes	characteristic
74	#15667945	C₂×C₄	1	1	yes	characteristic
75	#15667945	C₂×C₄	1	1	yes	characteristic
76	#15667945	C₂×C₄	1	1	yes	characteristic
77	#15667943	C₂×C₄	1	1	yes	characteristic
78	#15667943	C₂×C₄	1	1	yes	characteristic
79	#15667943	C₂×C₄	1	1	yes	characteristic
80	#15667943	C₂×C₄	1	1	yes	characteristic
81	#15667943	C₂×C₄	1	1	yes	characteristic
82	#15667943	C₂×C₄	1	1	yes	characteristic
83	#15667943	C₂×C₄	1	1	yes	characteristic
84	#15667943	C₂×C₄	1	1	yes	characteristic
85	C₄⋊#10623494	—	2	2	no	—
86	C₄⋊#10623494	—	2	2	no	—
87	#15667941	—	2	2	no	—
88	#15667941	—	2	2	no	—
89	C₂²⋊#10623494	—	2	1	no	—
90	C₂²⋊#10623494	—	2	1	no	—
91	C₂²⋊#10623494	D₄	1	1	yes	characteristic
92	C₂²⋊#10623494	D₄	1	1	yes	characteristic
93	C₂²⋊#10623494	D₄	1	2	yes	—
94	#15667923	—	2	2	no	—
95	#15667923	—	2	4	no	—
96	#15667922	—	2	2	no	—
97	C₄×#10623494	—	2	2	no	—
98	C₈×Dic₈₉	—	2	2	no	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	#117×C₈₉	—	2	1	no	—
102	#117×C₈₉	—	2	1	no	—
103	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
104	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
105	#117×C₈₉	C₂³	1	1	yes	characteristic
106	#117×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄²×C₈₉	—	2	1	no	—
112	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
113	C₂²⋊C₈×C₈₉	—	2	1	no	—
114	C₂²⋊C₈×C₈₉	—	2	1	no	—
115	#95×C₈₉	—	2	1	no	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂²×Dic₈₉	—	2	1	no	—
118	#13083558	—	2	2	no	—
119	#13083558	—	2	2	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
129	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
130	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂×D₄	1	2	yes	—
133	C₂×#10623494	C₂×D₄	1	2	yes	—
134	C₂×#10623494	#41	1	4	yes	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²⋊Dic₈₉	—	2	1	no	—
142	C₂²⋊Dic₈₉	—	2	1	no	—
143	C₂²⋊Dic₈₉	—	2	1	no	—
144	C₂²⋊Dic₈₉	—	2	1	no	—
145	C₄×Dic₈₉	—	2	1	no	—
146	C₄×Dic₈₉	—	2	1	no	—
147	C₄×Dic₈₉	—	2	1	no	—
148	C₄×Dic₈₉	—	2	1	no	—
149	C₂⁴×C₈₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	—	2	2	no	—
151	C₂²×C₄×C₈₉	—	2	2	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	2	no	—
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	M₁₆×C₈₉	—	2	2	no	—
162	M₁₆×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₄⋊C₄×C₈₉	—	2	1	no	—
165	C₄⋊C₄×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₈₉	—	2	1	no	—
171	C₂²⋊C₄×C₈₉	—	2	1	no	—
172	C₂²⋊C₄×C₈₉	—	2	1	no	—
173	C₂²⋊C₄×C₈₉	—	2	1	no	—
174	C₂²⋊C₄×C₈₉	—	4	2	no	—
175	C₄²×C₈₉	—	2	1	no	—
176	C₄²×C₈₉	—	2	1	no	—
177	C₄²×C₈₉	—	2	1	no	—
178	C₄²×C₈₉	—	2	1	no	—
179	C₄²×C₈₉	—	2	2	no	—
180	C₄²×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	—	4	1	no	—
184	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	2	1	no	—
197	C₂×C₄×C₈₉	—	2	1	no	—
198	C₂×C₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	4	2	no	—
201	C₂×C₄×C₈₉	—	4	2	no	—
202	C₂×C₄×C₈₉	—	8	1	no	—
203	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
209	C₂×Dic₈₉	—	2	1	no	—
210	C₂×Dic₈₉	—	2	1	no	—
211	C₂×Dic₈₉	—	2	1	no	—
212	C₂×Dic₈₉	—	2	1	no	—
213	C₂×Dic₈₉	—	4	2	no	—
214	C₂×Dic₈₉	—	8	1	no	—
215	C₈×C₈₉	—	4	2	no	—
216	#10623494	—	2	1	no	—
217	#10623494	—	2	1	no	—
218	#10623494	—	2	2	no	—
219	#10623494	—	2	2	no	—
220	#10623494	—	4	2	no	—
221	#10623494	#117	1	2	yes	—
222	#10623494	#117	1	2	yes	—
223	C₂²×C₈₉	—	2	1	no	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	—	2	1	no	—
228	C₂²×C₈₉	—	2	1	no	—
229	C₂²×C₈₉	—	2	1	no	—
230	C₂²×C₈₉	—	4	4	no	—
231	C₂²×C₈₉	#444	1	2	yes	—
232	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₈₉	#552	1	2	yes	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	4	1	no	—
237	C₄×C₈₉	—	4	1	no	—
238	C₄×C₈₉	—	4	1	no	—
239	C₄×C₈₉	—	4	1	no	—
240	C₄×C₈₉	—	8	2	no	—
241	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
242	C₄×C₈₉	#519	1	1	yes	characteristic
243	C₄×C₈₉	#547	1	2	yes	—
244	Dic₈₉	—	4	1	no	—
245	Dic₈₉	—	4	1	no	—
246	Dic₈₉	—	4	1	no	—
247	Dic₈₉	—	4	1	no	—
248	#22607	—	89	1	no	maximal, Sylow
249	C₂×C₈₉	—	2	2	no	—
250	C₂×C₈₉	—	2	2	no	—
251	C₂×C₈₉	—	4	1	no	—
252	C₂×C₈₉	#2344	1	1	yes	characteristic
253	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
254	C₂×C₈₉	#2957	1	1	yes	characteristic
255	#2924	—	89	1	no	—
256	#2924	—	89	1	no	—
257	C₂×#427	—	89	1	no	—
258	#1946	—	89	2	no	—
259	#1922	—	89	2	no	—
260	#1922	—	89	2	no	—
261	#1826	—	89	1	no	—
262	#1826	D₈₉	1	1	yes	characteristic
263	#1810	—	89	1	no	—
264	#1773	—	89	2	no	—
265	#1752	—	89	1	no	—
266	C₈₉	#22607	1	1	yes	characteristic, complemented, Sylow
267	C₂³×C₈	—	89	1	no	—
268	C₂×#117	—	89	1	no	—
269	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
270	#433	—	178	2	no	—
271	#433	—	178	2	no	—
272	#432	—	178	1	no	—
273	#432	—	178	1	no	—
274	#431	—	178	1	no	—
275	#431	—	178	1	no	—
276	C₂×#108	—	89	2	no	—
277	#427	—	89	1	no	—
278	#427	—	89	1	no	—
279	#427	—	89	1	no	—
280	#427	—	89	1	no	—
281	#427	—	89	1	no	—
282	#427	—	89	1	no	—
283	#427	—	89	1	no	—
284	#427	—	89	1	no	—
285	C₂×#107	—	89	1	no	—
286	C₂×#107	—	89	1	no	—
287	C₂×#106	—	89	1	no	—
288	C₂×#106	—	89	1	no	—
289	#424	—	89	2	no	—
290	#424	—	89	2	no	—
291	#407	—	89	1	no	—
292	#407	C₂×D₈₉	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	—	89	1	no	—
294	#405	—	89	2	no	—
295	#405	—	89	2	no	—
296	C₂×#97	—	89	2	no	—
297	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
298	#341	—	89	2	no	—
299	#339	—	89	2	no	—
300	#339	—	89	2	no	—
301	#339	C₂×D₈₉	1	2	yes	—
302	#339	C₂×D₈₉	1	2	yes	—
303	#336	—	89	2	no	—
304	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
305	C₂×M₁₆	—	89	2	no	—
306	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
307	C₂²×C₈	—	89	1	no	—
308	C₂²×C₈	—	89	1	no	—
309	C₂²×C₈	—	89	1	no	—
310	C₂²×C₈	—	89	1	no	—
311	C₂²×C₈	—	89	1	no	—
312	C₂²×C₈	—	89	1	no	—
313	C₂²×C₈	—	89	2	no	—
314	C₂²×C₈	—	178	4	no	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	89	1	no	—
318	#117	—	89	1	no	—
319	#117	—	89	1	no	—
320	#117	—	89	1	no	—
321	#117	—	178	1	no	—
322	#117	—	178	1	no	—
323	#117	C₄×D₈₉	1	1	yes	characteristic
324	#117	C₄×D₈₉	1	1	yes	characteristic
325	#117	C₂²×D₈₉	1	1	yes	characteristic
326	#117	C₂²×D₈₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	89	1	no	—
328	C₂×C₄⋊C₄	—	89	1	no	—
329	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	178	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	178	1	no	—
336	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
337	#108	—	178	4	no	—
338	#107	—	89	1	no	—
339	#107	—	89	1	no	—
340	#107	—	89	1	no	—
341	#107	—	89	1	no	—
342	#107	—	89	1	no	—
343	#107	—	89	1	no	—
344	#107	—	89	1	no	—
345	#107	—	89	1	no	—
346	#106	—	89	1	no	—
347	#106	—	89	1	no	—
348	#106	—	89	1	no	—
349	#106	—	89	1	no	—
350	#106	—	89	1	no	—
351	#106	—	89	1	no	—
352	#106	—	89	1	no	—
353	#106	—	89	1	no	—
354	C₄⋊C₈	—	178	2	no	—
355	C₄⋊C₈	—	178	2	no	—
356	C₄⋊C₈	—	178	2	no	—
357	C₄⋊C₈	—	178	2	no	—
358	C₂²⋊C₈	—	2	1	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	89	1	no	—
361	C₂²⋊C₈	—	89	1	no	—
362	C₂²⋊C₈	—	89	2	no	—
363	C₂²⋊C₈	—	178	1	no	—
364	C₂²⋊C₈	—	178	1	no	—
365	#97	—	178	4	no	—
366	#97	—	178	2	no	—
367	#97	—	178	2	no	—
368	C₄×C₈	—	178	2	no	—
369	C₄×C₈	—	178	2	no	—
370	#95	—	2	1	no	—
371	C₂⁴	#13083573	1	1	yes	characteristic
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	178	1	no	—
378	C₂²×C₄	—	178	1	no	—
379	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
382	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
383	C₂²×C₄	#13083573	1	1	yes	characteristic
384	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	178	2	no	—
388	M₁₆	—	178	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	89	1	no	—
391	C₂×C₈	—	89	1	no	—
392	C₂×C₈	—	89	4	no	—
393	C₂×C₈	—	89	1	no	—
394	C₂×C₈	—	89	1	no	—
395	C₂×C₈	—	89	2	no	—
396	C₂×C₈	—	89	2	no	—
397	C₂×C₈	—	178	2	no	—
398	C₂×C₈	—	178	2	no	—
399	C₂×C₈	—	178	2	no	—
400	C₂×C₈	—	178	2	no	—
401	C₂×C₈	—	178	2	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	89	1	no	—
408	C₄⋊C₄	—	89	1	no	—
409	C₄⋊C₄	—	89	1	no	—
410	C₄⋊C₄	—	89	1	no	—
411	C₄⋊C₄	—	178	1	no	—
412	C₄⋊C₄	—	178	1	no	—
413	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
416	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	178	1	no	—
423	C₂²⋊C₄	—	178	1	no	—
424	C₂²⋊C₄	—	178	1	no	—
425	C₂²⋊C₄	—	178	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	178	1	no	—
433	C₄²	—	178	1	no	—
434	C₄²	—	178	1	no	—
435	C₄²	—	178	1	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	#15667972	1	1	yes	characteristic
440	C₂³	#15667972	1	1	yes	characteristic
441	C₂³	C₂×#13083573	1	1	yes	characteristic
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	356	2	no	—
459	C₂×C₄	—	178	1	no	—
460	C₂×C₄	—	178	1	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	712	1	no	—
464	C₂×C₄	#15667972	1	1	yes	characteristic
465	C₂×C₄	#15667972	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
468	C₂×C₄	#41×D₈₉	1	2	yes	—
469	C₂×C₄	#15668059	1	2	yes	—
470	C₈	—	4	2	no	—
471	C₈	—	89	2	no	—
472	C₈	—	89	2	no	—
473	C₈	—	356	2	no	—
474	C₈	—	178	2	no	—
475	C₈	—	178	2	no	—
476	C₈	—	178	1	no	—
477	C₈	—	178	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	4	4	no	—
486	C₂²	#19151717	1	2	yes	—
487	C₂²	C₂×#15667972	1	1	yes	characteristic
488	C₂²	#19152285	1	2	yes	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	8	2	no	—
496	C₄	—	356	1	no	—
497	C₄	—	356	1	no	—
498	C₄	—	356	1	no	—
499	C₄	—	356	1	no	—
500	C₄	#117×D₈₉	1	1	yes	characteristic
501	C₄	#19152075	1	1	yes	characteristic
502	C₄	#19152246	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	4	1	no	—
506	C₂	#26023116	1	1	yes	characteristic
507	C₂	C₂×#19151717	1	1	yes	characteristic
508	C₂	#26029165	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1826	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂⁴×C₈₉	#41
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1826	D₈₉
hypocenter	C₈₉	#22607
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1826

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #26021004	C₂	semidirect
5. #26020854	C₂	semidirect
6. #26020849	C₂	semidirect
9. #26020135	C₂	semidirect
21. #19151634	C₄	semidirect
22. #19151634	C₄	semidirect
23. #19151634	C₄	semidirect
24. #19151634	C₄	semidirect
29. C₂×#15667945	C₄	semidirect
30. C₂×#15667945	C₄	semidirect
31. C₂×#15667943	C₄	semidirect
32. C₂×#15667943	C₄	semidirect
266. C₈₉	#22607	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26028912	2
#26028910	2
C₂×#19151634	2
#26021004	2
#26020854	2
#26020849	2
#26020352	2
#26020288	2
#26020135	2
#26020030	2
C₈₉×#1826	2
#22607	89